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Partition representations: Difference between revisions
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Partition representations (view source)
Revision as of 15:12, 16 December 2019
, 15:12, 16 December 2019→Mesh representation
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</source> | </source> | ||
{{Works in|[[J]]}} | {{Works in|[[J]]}} | ||
Here <source lang=j inline>-.</source> is [[ | Here <source lang=j inline>-.</source> is [[Not]], <source lang=j inline><</source> is [[Box]], and <source lang=j inline>;._1</source> uses the Cut operator <source lang=j inline>;.</source> with dropped initial elements. | ||
The [[Boolean]] control vector used by Mesh serves as another way to represent partitions. Unlike the case with [[Partitioned Enclose]], a Boolean vector here is sufficient to represent any partition including those with empty divisions. This is possible because of the vector's increased length: while Partitioned Enclose uses only one Boolean for each element in the partitioned vector, the mesh vector has a 1 for each element in the partitioned vector as well as a 0 for each divider. | The [[Boolean]] control vector used by Mesh serves as another way to represent partitions. Unlike the case with [[Partitioned Enclose]], a Boolean vector here is sufficient to represent any partition including those with empty divisions. This is possible because of the vector's increased length: while Partitioned Enclose uses only one Boolean for each element in the partitioned vector, the mesh vector has a 1 for each element in the partitioned vector as well as a 0 for each divider. | ||
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1 1 1 0 0 1 0 1 1 0 | 1 1 1 0 0 1 0 1 1 0 | ||
</source> | </source> | ||
In the above functions, the only difference in code is exchanging 0 and 1, and the only difference in output is an extra trailing 0 when computed from the division lengths. The mesh representation makes the partition representation duality especially clear, as the dual representation can be obtained simply by [[ | In the above functions, the only difference in code is exchanging 0 and 1, and the only difference in output is an extra trailing 0 when computed from the division lengths. The mesh representation makes the partition representation duality especially clear, as the dual representation can be obtained simply by [[Not|negating]] the mesh vector. | ||